2015/01/17 by Ryuhei Mori, Mori, Ryuhei · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech #cs.IT #math.IT #quant-ph
paper · pdf · doi:10.48550/arxiv.1501.04183
6 pages, to appear in ISIT 2015
openalex publication_date 2015/01/17 · arxiv created 2015/04/24 · arxiv updated 2015/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The holographic transformation, belief propagation and loop calculus are generalized to problems in generalized probabilistic theories including quantum mechanics. In this work, the partition function of classical factor graph is represented by an inner product of two high-dimensional vectors both of which can be decomposed to tensor products of low-dimensional vectors. On the representation, the holographic transformation is clearly understood by using adjoint linear maps. Furthermore, on the formulation using inner product, the belief propagation is naturally defined from the derivation of the loop calculus formula. As a consequence, the holographic transformation, the belief propagation and the loop calculus are generalized to measurement problems in quantum mechanics and generalized probabilistic theories.